In any discussion of tire balancing “best practice” it is worth repeating that the best involves using a modern Hunter Tire Balancing machine.
If a tire shop is not using a modern Hunter it would not surprise me that they also make bad decisions about the details of making sure an adhesive weight stays on.

I have never used the tire pellets but in the late 1970s I bought four behind the wheel spacers with steel pellet in oil that were an improvement. After about six years of use one of the four spacers began to leak oil. I later thought about buying some of the mercury filled balancing units.

It has been my experience that Bridgestone brand tires come from the factory better balanced, including being better than cheaper tire brands that Bridgestone’s parent company also owns.

In the 1980s I had to learn balancing of electric motor rotors, then huge roots blower vacuum pumps, then large fans and centrifuges. Balancing is challenging if you have to do the math by hand. I still own a 12 volt portable electronic strobe with digital rpm readout, which helps a lot to spot problems, but becomes highly dangerous when you can forget “stopped motion” fools you into sticking your hand into a spinning machine.